Blanc, 26, is due to hold events in Lyon on October 20th and Paris on the 21st.
The controversial dating coach, has already been banned from Australia, the UK and Singapore over concerns that his talks incite sexual violence.
France may be the next country to close its borders to the Swiss-born US-based pick-up 'artist' Blanc.
The petition, called “Intervene to stop Julien Blanc’s conferences being held in France” and aimed at Pascale Boistard, the Secretary of State for Women’s Rights, had attracted over 6,200 signatures by Thursday morning.
On Wednesday Boistard tweeted her support for the petition.
“Thank you for your vigilance. I am looking at ways to act to stop all speeches inciting rape or acts of violence,” she wrote.
#StopJulienBlanc, merci de votre vigilance. J'examine les moyens d'action pour empêcher tout discours d'incitation au viol et aux violences
— Pascale Boistard (@Pascaleboistard) January 28, 2015
In November last year a similar campaign was started in Sweden to stop Blanc at the border if he tried to arrive in the country for several tour dates he had planned, including one in Gothenburg.
Later that week the scheduled tour dates had been removed from Blanc’s official website, suggesting that the petition had been successful.
Blanc works for LA-based company Real Social Dynamics and travels the world telling men how to seduce "any woman they want".
However some critics have branded his tactics sexist and at times violent and dangerous.
Online seminars hosted by the coach include scenes where he grabs the necks of women and pushes their faces towards his crotch.
He also tells a group of men: "In Tokyo, if you're a white male, you can do what you want."